What's Wrong with my Internet? - 1

I have an AT&T U-verse router/modem setup whatever. Every minute or so (occasionally every ten seconds or so) the internet will just drop from my computer. It has happened on two different computers (both HP laptops, one I've had for years, and a newer one), and occasionally happens on the desktop (Dell) it's immediately connected to. It happens on my iPhone occasionally as well.

For whatever reason, while I am steaming (LoL, WoW, GW2, etc.) it's totally fine; just not when I'm on YouTube watching videos/web browsing. It's INCREDIBLY annoying.

I've got an HP desktop shipping to me right now. Is the problem the router/modem shizzle, or is it that HP has bad wifi cards (or whatever tat it is)? It would be a major inconvenience to run an Ethernet cord to my room from the computer room as it would span a hallway.

Model number for the modem is NVG510.

Thank you for all answers; they are greatly appreciated. :]
Have a great day.

Sounds like the router, as that's the common factor. Have any of the router settings been changed recently? Could it be going into power-saving mode?
Maybe your network provider has a helpline that will help diagnose the problem?
Failing that, could you borrow another router from someone to check if that solves it?